Self-propulsion near the onset of Marangoni instability of deformable active droplets

TL;DR

This paper uses weakly nonlinear analysis to study how deformability affects the onset of self-propulsion in chemically active droplets near Marangoni instability, revealing that deformability can enhance or hinder propulsion and alter bifurcation types.

Contribution

It provides the first asymptotic analysis of self-propulsion near the instability threshold considering droplet deformability, highlighting its impact on propulsion and bifurcation nature.

Findings

Deformability enhances propulsion for viscous droplets near threshold.

Deformability hinders propulsion for less viscous droplets.

Bifurcation type changes from transcritical to subcritical with increased deformability.

Abstract

Experimental observations indicate that chemically active droplets suspended in a surfactant-laden fluid can self-propel spontaneously. The onset of this motion is attributed to a symmetry-breaking Marangoni instability resulting from the nonlinear advective coupling of the distribution of surfactant to the hydrodynamic flow generated by Marangoni stresses at the droplet's surface. Here, we use weakly nonlinear analysis to characterize the self-propulsion near the instability threshold and the influence of the droplet's deformability. We report that in vicinity of the threshold, deformability enhances self-propulsion of viscous droplets, but hinders propulsion of drops that are roughly less viscous than the surrounding fluid. Our asymptotics further reveals that droplet deformability may alter the type of bifurcation leading to symmetry breaking: for moderately deformable droplets the onset of self-propulsion is transcritical and a regime of steady self-propulsion is stable; while in the case of highly deformable drops, no steady flows can be found within the asymptotic limit considered in this paper suggesting that the bifurcation is subcritical.